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geographic grid with latitude
φ
and longitude
ʻ
, divided into steps of
ʔφ
and
ʔʻ
,
respectively. In this study, it is supposed
ʔφ
=
ʔʻ
= 0.1
°
. As result, the area
. The cells
,
P
k¼1
r
k
¼
r
N
X
¼
[
i
¼
1
X
k
where
X
k
is part of
Ω
with area
˃
k
=
ʔφ ʔʻ
X
k
are situated along the AYRS beginning with
Ω
1
at the Angara river source up to
Ω
N
in the Yenisey River mouth. The procedure of spatial discretization is provided
by the IAS block via, including in the AYRSSM database the set of identi
ers
a
ij
A
k
¼
, 5. The hydrology regime of the AYRS is described by the
schematic diagram of Fig.
6.14
. The equations for this scheme can now be written
in the form of balance correlations on each of the
, k =1,
…
X
k
(k =1,
…
, N):
r
k
@
W
@
t
þ n
u
@
W
@u
þ n
k
@
W
@k
¼ V
B
r
k
þ
D
þ
T
þ
L
ð
6
:
17
Þ
q
k
r
k
@
C
@
t
þ l
@
C
¼
q
k
r
k
B
þ
J
þ
K
V
U
F
M
R
ð
6
:
18
Þ
@
x
ð
1
q
k
Þr
k
d
dt
¼ U
þ
F
þ
M
þ
N
þð
1
q
k
Þr
k
B
T
L
K
P
ð
6
:
19
Þ
r
k
@
G
@
t
þ
v
u
@
G
@u
þ
v
k
@
G
@k
¼ R
þ
P
J
N
D
ð
6
:
20
Þ
ʾ
φ
and
ʾ
ʻ
are the projections of the wind speed,
ˁ
k
is the part of the area
Ω
k
where
ʼ
occupied by the river,
is the river speed, v
φ
and v
ʻ
are the speed projections of the
ground water motion, x is the direction of river
fl
flow, and t is time.
(
6.20
) are described by mathe-
matical expressions in accordance with the papers by Krapivin et al. (1996) and
Bras (1990). Appropriate models are given in Table
6.13
. There are many real-
izations for some of these functions. This provides the user of the AYRSSM with
the possibility of forming scenarios for the computer experiments. Values of
The functions on the right side of Eqs. (
6.17
)
-
ʾ
,
ʼ
and v were estimated on the basis of the Irkutsk Scienti
c Center database. It is
possible for the user to vary these parameters during the calculation process. In this
study, average values of these parameters are estimated by
ʾ
= 3.3 m/s,
ʼ
= 1.7 m/s
and v = 0. Variations of the parameter
are realized by adaptation of the left part of
Eq. (
6.18
) to the empirical data illustrated in Fig.
6.13
. Boundary conditions for
Eqs. (
6.17
)
ʼ
(
6.20
) are formed by the global model (Krapivin 1993). Soil moisture
transport between the cells
-
X
k
is neglected. Synoptic situations are described by a
discrete scheme with temporal parameters t
i
(i =1,
, 4), where t
1
is the beginning
of the summer period, t
2
is the start of winter, t
3
is the end of winter, and t
4
is the
time of the spring thaw when the snow and ice are melting. Between these times the
synoptical situation does not change.
In the common case, the vertical structure of the river water area in
…
,
N) is described by block SES (Krapivin 1995). A snow layer of thickness g
k
is
formed at the expense of
X
k
(k =1,
…
fl
ow B
k
according to:
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